Force versus deformation measurement

The classic way that we perform force versus deformation measurements is to deform a sample at a constant rate, while we record the force induced within it. We normally carry out such tests in one of three configurations tensile, compressive, or flexural, which are illustrated in Fig. 8.1. We can also test samples in torsion or in a combination of two or more loading configurations. For the sake of simplicity, most tests are uni-axial in nature, but we can employ bi-axial or multi-axial modes when needed,... 

This chapter comprises two sections. The first describes the most usual techniques to directly measure force versus distance profiles between solid or liquid surfaces. We then describe different long-range forces (range >5 nm) accessible to evaluation via these techniques for different types of surface active species. The second section is devoted to attractive interactions whose strong amplitude and short range are difficult to determine. In the presence of such interactions, emulsion droplets exhibit flat facets at each contact. The free energy of interaction can be evaluated from droplet deformation and reveals interesting issues. 

Force versus displacement data are directly useful in comparing some simple mechanical properties of particles from different samples, for example, the force required to break the particle and the deformation at breakage. However, these properties are not intrinsic, that is, they might depend on the particular method of measurement. Determination of intrinsic mechanical properties of the particles requires mathematical models to derive the stress-strain relationships of the material. 

Israelachvili and coworkers [64,69], Tirrell and coworkers [61-63,70], and other researchers employed the SFA to measure molecular level adhesion and deformation of self-assembled monolayers and polymers. The pull-off force (FJ, and the contact radius (a versus P) are measured. The contact radius, the local radius of curvature, and the distance between the surfaces are measured using the optical interferometer in the SFA. The primary advantage of using the SFA is its ability to study the interfacial adhesion between thin films of relatively high... 

The temperature dependence of birefringence and stress vi/ere measured under the conditions of constant force or constant deformation of the sample. Both experimental techniques lead to the same results of the quotient An/X -X" The stress - strain and birefringence - strain measurements do not differ from these generally received for common rubbers, vi/here cr and An linearly depend on the deformation factor (X -X M. With respect of the formation of the anisotropic phase at lovi/ temperatures especially the temperature dependence of An and cr are of interest. Therefore in order to obtain results vi/hich are comparable i/ith results of amorphous rubbers having no mesogenic side chains wie plotted the product CT versus temperature. 

Measurements from the SFA have been analysed in two primary ways. In the first, the data is plotted as F/R versus d. F is the force measured as described above, d is the distance of separation between the surfaces and R is the radius of curvature of the lens/sample. A sample plot is shown in Fig. 2. The second way is the use of contact mechanics . This discipline analyses the deformation of elastic bodies in contact. There are two main methods for analysing contact mechanics data. One is known... 

When discussing the theory of rubber elasticity in Chapter 10, we were concerned with fairly large extensions or strains. These arose because polymer molecules could uncoil at temperatures above T. For materials used as structural elements (such as glassy polymers), we usually cannot tolerate strains of more than a fraction of 1%. Therefore, it is customary to employ measures of infinitesimal strain. In a tensile test, we usually take a specimen with tabs at the ends and stretch it, as shown in Figure 12.1. One end of the sample is typically fixed, whereas the other is moved outward at a constant velocity. The force F necessary to carry out the stretching deformation is monitored as a fimction of time along with the instantaneous sample length, L. From the measured load versus extension behavior, we can calculate the stress and strain as follows ... 

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